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# Factorising 4th degree polynomials? watch

1. I need to Show that X^4+5x^3+6x^2-4x-8= (x^2+x-2)(x^2+4x+4)

but I am not too sure how to go about doing this- I was thinking of doing long division and then obtaining a polynomial with 3rd degree?
2. (Original post by FloralEssence)
I need to Show that X^4+5x^3+6x^2-4x-8= (x^2+x-2)(x^2+4x+4)

but I am not too sure how to go about doing this- I was thinking of doing long division and then obtaining a polynomial with 3rd degree?
If the question does say "show" then all you need to do is expand the right-hand-side and show it equals the left.

It would be good if you post a picture of the question or post the question exactly as you see it (if you haven't already).
3. (Original post by FloralEssence)
I need to Show that X^4+5x^3+6x^2-4x-8= (x^2+x-2)(x^2+4x+4) but I am not too sure how to go about doing this- I was thinking of doing long division and then obtaining a polynomial with 3rd degree?
You could expand RHS. Or Look at the RHS find suitable factor e.g. (x-1) and use the factor theorem to show when x=1 f(x) is 0 then do algebraic division and repeating substituting in suitable values
4. (Original post by notnek)
If the question does say "show" then all you need to do is expand the right-hand-side and show it equals the left.

It would be good if you post a picture of the question or post the question exactly as you see it (if you haven't already).
Hey!
This is the question, and I am asked to prove from left to right, i.e. do the factorisation of some sort such that I may obtain the RHS

Show x^4 + 5x^3 + 6x^2 −4x−8 = (x^2 + x−2)(x^2 + 4x + 4). Hence sketch the curve y = f(x)where f(x) = x4 +5x3 +6x2−4x−8, showing all points of interest.
5. (Original post by FloralEssence)
Hey!
This is the question, and I am asked to prove from left to right, i.e. do the factorisation of some sort such that I may obtain the RHS

Show x^4 + 5x^3 + 6x^2 −4x−8 = (x^2 + x−2)(x^2 + 4x + 4). Hence sketch the curve y = f(x)where f(x) = x4 +5x3 +6x2−4x−8, showing all points of interest.
As I said before, since you're given the factorisation and are asked to "show", you just need to expand the brackets and show that this is equal to the polynomial.
if the exams come and ur stuffed while trying to answer one just go with the good ol' factor theorem. Find what x values give f(x)=0, -ve value is the factor, find as many simple ones as you can and you either multiply some brackets or re-arrange a couple. (4 brackets has more than 1 configuration therefore multiple [equivalent] quadratic factors)
7. (Original post by Xenon17)
You could expand RHS. Or Look at the RHS find suitable factor e.g. (x-1) and use the factor theorem to show when x=1 f(x) is 0 then do algebraic division and repeating substituting in suitable values
Yeah, this was what I have been trying to do

I managed to get x^3+6x^2+12x+8

then, I continued- I found that x-2 was a factor of the above result.

I did long division and obtained x^2+4x+4

-----------------------------------

EDIT:

Oh, guys, I found the result! sorry- I multiplied the factors (x-1)(x-2) out and got x^2+x-2

then pairing up with x^2+4x+4

Thanks to the contributers!

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